Procedure:

Cut stew beef into bite size pieces. Usually cutting each piece in half is sufficient. Brown meat with about one fourt of the diced bell pepper and onion, one or two of the garlic cloves, and spices to taste (some of the peppers, a little chili powder works great).

When the stew beef is lightly browned, drain it and place it and all other ingredients, except for the tomato paste, into a large pot. (A crock-pot works just fine as well) Stir together, mixing all of the ingredients.

Spice to taste. Go easy on the pepper; the combination of the three should be about 1 teaspoon black pepper (or a little more) to about 1/2 teaspoon of the red and white peppers. Remember, with all that garlic and the bell peppers, the spices are going to be secondary to the natural flavors of the major ingredients.

Cook covered on as low of a heat as possible (1 or 2 on an electric range), stirring Hourly at most for ten to twelve hours, or until everything is the same brownish color and you're really hungry.
The longer it cooks, the more tender the meat will be, and the more subtle and mellow the flavorings will become.
Roughly 30 minutes before serving, mix in the can of tomato paste, if the chili is not thick enough for your tastes.